Molecular Order Determines Gas Transport through Smectic Liquid Crystalline Polymer Membranes with Different Chemical Compositions

: Amorphous polymers are often used for gas separation but have a trade-off between gas permeability and selectivity. Here, the effect of chemical composition and temperature on gas permeability and solubility in well-ordered LC polymer membranes is investigated. Membranes with various compositions of a monomethacrylate LC ( M1 ) with a crown ether functionality to enhance CO 2 solubility and a smectic diacrylate ( M2 ) cross-linker were fabricated, while all having the same order (smectic C) and alignment (planar). Single gas sorption and permeation data show for the membranes with 30 wt % M1 a higher CO 2 solubility coefficient compared to membranes without M1 , which results in a higher CO 2 permeability and selectivity. For membranes that contain more than 30 wt % M1 decreasing layer spacings lead to reduced gas solubilities that result in lower gas permeabilities without additional selectivity gain toward CO 2 . The effect of temperature is demonstrated by comparing single gas sorption and permeation data below and above the T g of the membranes. The diffusion coefficient increases above the T g of the membranes with increasing M1 content leading to higher CO 2 permeabilities and selectivities. These results show that not only the chemical composition but also the layer spacing of the smectic structures determines the gas separation performance of smectic LC polymer membranes.


INTRODUCTION
The tremendous increase of greenhouse gas emissions such as CO 2 , CH 4 , and NO x from the incineration of fossil fuels for large-scale energy production and industrial activities results in great challenges for the sustainable development of our modern society. 1 Valuable gas sources such as natural gas and biogas or waste streams like flue gases contain large amounts of greenhouse gases.−5 The most used methods to separate gases include cryogenic distillation, amine absorption, pressure swing adsorption, and membrane separations. 3,5,6−8 Despite that polymeric membranes are often used for gas separations, most of the used polymers are not highly ordered at a molecular level.−13 Controlling the membrane building blocks at a molecular level is a tool to improve membrane performances.
Self-assembly of liquid crystalline (LC) polymeric materials provides control over the supramolecular organization and alignment of the building blocks at the molecular level and can be used for membrane applications. 9,14−16 A variety of ordered nanostructures can be obtained, which, depending on the positional order of the LC monomers and the fabrication process, can differ in molecular order and orientation.Subsequent cross-linking of the LC monomers fixates the nanostructures and results in robust free-standing LC polymer membranes.Although LC polymer membranes have already been investigated for water separations, 17−30 these materials are hardly investigated for gas separations. 9,15,31In a very recent publication we reported the gas separation perform-ances of smectic LC polymer membranes by molecular engineering. 31In other work, we studied the role of supramolecular organization and orientation in free-standing thermotropic LC polymer membranes based on crown ether functionalized LCs for gas separation by using LC membranes with various distinct morphologies and alignment while using the same chemical composition (Figure 1a for chemical structures). 15We found that control over the molecular order and orientation of the LC building blocks are important parameters that influence the gas separation performances to a great extent.Increasing the molecular order leads to lower gas permeabilities but higher gas selectivities.It was hypothesized that with increasing the molecular order in the membranes gas diffusion was reduced.The smaller free volume elements in the more ordered smectic C (lamellar structures) membranes hinder gases with larger kinetic diameters (N 2 ) more than gases with smaller kinetic diameters (He and CO 2 ), resulting in lower gas permeabilities but higher selectivities.Furthermore, the orientation of the lamellar structures highly influences gas permeability and ideal gas selectivity.Membranes with the lamellar structures perpendicular to the permeation direction (homeotropic alignment) exhibit higher permeation resistances that result in reduced gas diffusion and lower gas permeabilities compared to membranes with the lamellar structures parallel to the permeation direction (planar alignment).−36 Moreover, the gas separation performances of polymeric membranes are greatly affected by temperature, especially when crossing the glass transition temperature (T g ). 6,37,38However, this effect was never investigated for LC-based polymer membranes.
Here we thus study the effect of chemical composition and temperature on gas permeability and solubility in free-standing thermotropic LC polymer membranes with planar aligned smectic morphologies for gas separations of He, CO 2 , Ar, and N 2 (Figure 1b).Well-aligned LC membranes with various compositions of a monomethacrylate (M1) LC with a crown ether functionality and a smectic diacrylate (M2) cross-linker are fabricated and characterized.The effect of chemical composition on the gas separation performances of LC membranes is investigated by measuring the single gas sorption and permeation of various gases.The effect of temperature on the membrane performance is shown by comparing single gas performances below and above the T g of the membranes.

LC Polymers.
LCs are molecules that have additional phases (mesophases) between the conventional isotropic liquid and anisotropic crystalline solid phase that combine the mobility of liquids with a degree of long-range positional and orientational order like in solids while maintaining a liquid consistency. 14,39Thermotropic calamitic (rod-shaped molecules) LCs can self-assemble in various distinct organizations like nematic and smectic mesophases that differ in molecular order, when heating or cooling the material.The smectic mesophase is a more ordered phase compared to the nematic phase, as it has not only orientational order along the axis of the molecules (common molecular director) but also position- al order of the center of mass over the long axis leading to lamellar layers with a discrete layer spacing.Besides control over the supramolecular organization of the LCs, the molecular orientation of the LCs can also be controlled.Aligning the LCs perpendicular to the permeation direction (planar alignment) results, for a smectic mesophase, in lamellar structures that are parallelly oriented to the permeation direction, while aligning the LCs parallel to the permeation direction (homeotropic alignment) results in lamellar structures that are perpendicularly oriented to the permeation direction. 14The orientation of the formed nanostructures highly influences gas permeability and selectivity by affecting the diffusion coefficient.Homeotropic alignment results in a higher diffusion resistance and therefore lower permeabilities but higher selectivities compared to planar alignment. 15Small LC molecules are easier to align compared to LC polymers.However, the self-assembled structures are not durable and do not give mechanical strength for membrane applications.Therefore, LC molecules are equipped with reactive end groups to fixate the self-assembled morphology by a polymerization reaction resulting in robust polymer membranes.
2.2.Membrane Gas Separation.In gas separation nonporous (dense) membranes are predominantly used to separate different gases.Gas transport through dense membranes is best described by the solution-diffusion model, which states that gas transport occurs in three steps: (1) sorption of gases onto the membrane surface, (2) diffusion of the gases through the thickness of the membrane, and last (3) desorption at the permeate side of the membrane. 40,41The permeability (P i ), which is commonly used to express the membrane performance, is defined as the product of the diffusivity (D i ) and the solubility (S i ) of a certain gas species ( eq 1).
where P i is the permeability of gas species i (barrer (10 −10 cm 3 (STP)•cm/(cm 2 •s•cmHg))), J i is the flux (cm 3 (STP)/cm 2 •s), L is the thickness of the membrane (cm), P i, feed is the feed pressure (cmHg), and P i, permeate is the permeate pressure (cmHg).The ideal selectivity of gas species i with respect to gas species j, α i/j (−), is calculated with the pure gas permeability of gas species i and j (eq 2).
−44 According to the solution-diffusion model, dense polymer membranes separate gases via their intrinsic differences in diffusivity and solubility.However, these parameters are bulk parameters and affected by many variables.The diffusion coefficient mainly depends on the free volume in the polymers and the size of the gaseous penetrant, where high amounts of free volume and smaller gas molecules usually result in higher diffusion coefficients compared to low amounts of free volume and larger gases. 45The solubility coefficient mainly depends on the condensability of the gas and the chemical affinity between the gas molecules and the membrane matrix.The condensability depends on the critical temperature of the gas and usually increases with increasing critical temperature. 46Gas solubility can be enhanced when there is a chemical affinity between the penetrant and the polymer phase. 6,37,38−36 Permeation is a thermally activated process and is therefore highly dependent on temperature.The temperature dependence of both gas diffusion and solubility follows an Arrhenius type of equation, but the activation energy for these processes is affected differently. 37,47Diffusion is generally a stronger function of temperature than solubility, and diffusion typically increases considerably with increasing temperature, while solubility decreases with increasing temperature.As a result, gas permeability usually increases with temperature.Moreover, the diffusion coefficient is dependent on the free volume that is available for diffusion, which greatly depends on temperature as well the T g of the polymer. 38,46,48Above the T g , where the polymer is in its rubbery state, large-scale segmental motion of the polymer chains results in high amounts of free volume that lead to higher diffusion coefficients and gas permeabilities, but usually also in low selectivities.Below the T g the polymer is in its glassy state, and thermal motion of the polymer chains is restricted, which results in low diffusion coefficients and gas permeabilities but high selectivities.Therefore, the overall performance of a membrane can be tuned (i.e., the permeability) by changing the operating temperature to below or above the T g of the polymer.

Synthesis of M1 and M2. 4-((11-Methacryloylundecan-1yl)oxy)-4′-(4′-carboxybenzo-15-crown-5)biphenyl (M1). 4-((11-
Methacryloylundecan-1-yl)oxy)-4′-(4′-carboxybenzo-15-crown-5)biphenyl (M1) was synthesized as described in the literature. 15,49The characterization data are in accordance with the literature. 15is (4-((11-(acryloyloxy)undecyl)oxy)phenyl) Terephthalate (M2).Bis(4-((11-(acryloyloxy)undecyl)oxy)phenyl) terephthalate (M2) was synthesized as described in the literature. 15The characterization data are in accordance with the literature. 15.3.Membrane Preparation.LC mixtures consisting of various M1/M2 compositions (Figure 1a shows the chemical structures of M1 and M2; Table 1 presents the used ratios of M1 and M2), 0.5 wt % Irgacure 819 as photoinitiator and 0.1 wt % TBHQ as inhibitor were prepared by dissolving the compounds in chloroform and subsequently removing the solvent.Membranes with a thickness of 20 ± 0.4 μm were prepared by heating an LC mixture above its isotropic phase (process temperature in Table 1) and using capillary suction between two glass plates with 20 μm spacers to fill the glass cells.To control the alignment of the samples and obtain planar alignment, the glass plates were functionalized with a rubbed polyimide layer (Optimer AL 1254; JSR Corporation, Tokyo, Japan).After the glass cells were filled, the samples were placed inside a temperaturecontrolled box with an N 2 flow at 140 °C for the 0/100 and 30/70 compositions and 130 °C for the 50/50, 60/40 and 70/30 compositions.The samples were left 5 min at the above-mentioned temperature before they were cooled to the smectic phase using a cooling rate of 3 °C/min.Subsequently, the samples were photopolymerized by illuminating the samples for 10 min under an unfiltered spectrum of a collimated EXFO Omnicure S2000 UV lamp with a light intensity of 20 mW/cm 2 in the range 320−390 nm.The samples were removed from the N 2 box and allowed to cool to room temperature.Free-standing membranes were obtained by immersing the samples for 10 min in water at 80 °C and subsequently opening the glass cells.
3.4.Characterization.Attenuated total reflection Fourier transform infrared spectroscopy (ATR FT-IR) spectra, polarizing optical microscopy (POM) images, differential scanning calorimetry (DSC) measurements, and medium-and wide-angle X-ray scattering (MAXS/WAXS) measurements have been carried out according the same procedure as described in the literature. 15,31.5.Gas Sorption.Gas sorption of CO 2 was measured with a Rubotherm series IsoSORP sorption instrument at 6 bar and 20, 40, and 70 °C to determine the solubility coefficient of all membranes.The measurement procedure and solubility coefficients of CO 2 were determined according the same procedure as described in our previous publications. 15,31The equilibrium time of each measurement, which was determined by monitoring the sorption over time, was 3 h.
3.6.Single Gas Membrane Performances.Single gas permeation experiments using He, CO 2 , Ar, or N 2 were performed in a custom-built permeation setup and have been performed according a procedure described in our previous publications. 15,31ingle gas permeabilities were determined from the steady-state pressure increase in time in a calibrated volume at the permeate side of the membrane at temperatures of 20, 40, and 70 °C and a feed pressure of 6 bar.The order in which the gases were measured was kept constant (He, Ar, N 2 , and CO 2 ) since CO 2 could induce swelling of the membrane.CO 2 diffusion coefficients of the membranes were calculated using eq 1.The ideal gas selectivities were calculated with eq 2.

Preparation and Characterization of Liquid Crystalline Mixtures and Membranes.
A photopolymerizable nematic monomethacrylate with a crown ether functionality (M1) and a smectic diacrylate cross-linker (M2) were synthesized and characterized as described in the literature (Figure 1a). 15,49M1 was selected for its cyclic oligoethylene oxide segments, which are known for the favorable interactions with CO 2 leading to an enhanced CO 2 solubility, 32−36 while M2 was selected for its stable smectic phase and to improve the mechanical strength of the fabricated membranes.The phase transitions of both M1 and M2 are in accordance with previously reported literature. 15C mixtures with various compositions of M1 and M2, a photoinitiator, and an inhibitor were prepared and characterized with DSC and POM to determine the corresponding phase transitions (for DSC and POM see Figures S1−S5; for phase transition values see Table S1).Compositions containing more than 70 wt % M1 did not exhibit a stable smectic mesophase but only a broad nematic mesophase.Because our previous study showed that the gas separation performances of LC membranes are highly influenced by the membrane morphology, only mixtures that exhibit a smectic mesophase were used to prepare membranes to study the effect of chemical composition and temperature on the gas separation performances of LC membranes. 15C membranes were prepared by incorporating the LC mixtures in glass cells having an alignment layer to obtain planar alignment.The LC mixtures were polymerized in their smectic phase to fixate the lamellar morphology, and after opening of the cells, free-standing membranes were obtained (see Figure 1b,c for an artist impression of the top and crosssection view of a free-standing membrane with a smectic C morphology).FTIR before and after polymerization confirmed the full conversion of the acrylate moieties (Figure S6).
The orientation and organization of the membranes were investigated with POM and XRD (see Figure S7 for POM images).POM shows the planar alignment of the membranes with dark images under parallel conditions and bright images under 45°tilt, indicating that the membranes are well oriented.Wide-angle X-ray scattering (WAXS) and medium-angle X-ray scattering (MAXS) were measured to determine the morphology and alignment of the membranes at 20 °C and are shown in Figure 2.
The 2D WAXS and MAXS spectra of all membranes contain diffraction spots that indicate that all molecules are oriented in  a common direction.All MAXS spectra diffraction spots parallel to the alignment direction, which corresponds to an ordered smectic C morphology.The tilt angle of the tilted layered structures is found to be highly dependent on the chemical composition and varies between 18°for the membranes without M1 (0/100) and 32°for the membranes that contain 70 wt % M1 (70/30).Moreover, the layer spacing, which corresponds to the spacing between two layers, was determined for all compositions and is shown in Figure 3.
Figure 3 shows that the layer spacings of membranes without M1 (0/100) and 30 wt % M1 (30/70) are similar as the theoretical length of M2 (49.9 Å) that connects the lamellar structures and is therefore expected to mainly determine the layer spacing.However, for membranes that contain more than 30 wt % M1, the layer spacing starts to decrease.This can be explained because the length of M1 (theoretical length is 28.1 Å) is smaller than that of M2, making the layer spacings smaller with higher M1 contents.The intermolecular spacing that corresponds to the intermolecular stacking of the LC building blocks is not affected by the chemical composition and was similar for all compositions (varying between 4.5 and 4.8 Å).The above confirms the formation of a planar aligned smectic C morphology for all M1/M2 compositions at 20 °C.
To study the effect of temperature on membrane morphology, the thermal properties of the membranes with various M1/M2 compositions were measured with XRD and DSC.The membrane morphology was studied by measuring WAXS and MAXS spectra of membranes without M1 (0/100) and 70 wt % M1 (70/30) at 20 and 70 °C (see Table S2 for tilt angle, layer spacings, and intermolecular spacing).WAXS and MAXS spectra of membranes with both compositions (0/100 and 70/30) show similar morphologies, tilt angles, layer spacings, and intermolecular spacing at 20 and 70 °C.This means that within this temperature range the membrane morphology is independent of temperature.Although membranes with 70 wt % M1 (70/30) are less cross-linked compared to membranes without M1 (0/100), these results show that 30 wt % cross-linker (M2) is sufficient to fixate the membrane morphology.DSC measurements show a weak signal between 46 and 55 °C that represents the glass transition temperature (T g ) of the membranes.The results are shown in Table 2

(see Figures S8−S12 for DSC spectra).
Table 2 shows that the membranes without M1 (0/100) exhibit the highest T g (55 °C) of all membranes.This is as expected because these membranes have the highest cross-link density of all membranes, which restricts the mobility of the polymer chains that leads to a higher T g . 50For the membranes with M1, the cross-link density decreases with increasing M1 content leading to higher polymer chain mobility and thereby lowering the T g (46 °C for the membranes with 70 wt % M1).Remarkably, the T g of the membranes with respectively 30 wt % (30/70) and 70 wt % M1 (70/30) only shows a difference of 1 °C, indicating that the cross-link density only has a slight effect on the T g .

Effect of M1/M2
Composition on Single Gas Performances.The effect of the chemical composition on the gas permeation performances of the LC membranes was investigated by measuring single gas permeation of He, CO 2 , Ar, and N 2 at 20 °C for all membranes.To show the effect of M1 in more detail, the permeation data and ideal gas selectivities are normalized to the membranes without M1 (absolute permeability values of 0/100 are 1.21, 0.34, 0.05, and 0.02 barrer for He, CO 2 , Ar, and N 2 , respectively).The results are shown in Figure 4 (see Tables S3 and S4 for all permeation and ideal selectivity values).
Figure 4a shows that the normalized permeability of CO 2 increases for membranes that contain 30 wt % M1.This increase in CO 2 permeability can be attributed to the favorable interactions of the quadrupole of CO 2 with the dipole moments of the crown ether moieties in M1. 1,32 Surprisingly the normalized Ar permeability also slightly increases while it has no favorable interactions with the crown ether moieties.At higher M1 content, the CO 2 and Ar permeability decreases again.Similarly, the permeability of all other gases decreases over the full range.WAXS and MAXS measurements (section 4.1) show that the layer spacing for the membranes that contain 30 wt % M1 is equal to that of the membranes without M1 but starts to decrease with increasing M1 content.It is likely that a decreasing layer spacing also decreases the overall free volume within the membrane, which can affect solubility and therefore result in lower gas permeabilities. 51The normalized ideal gas selectivities in Figure 4b show that the He/N 2 selectivity is independent of the composition, elucidating that the relative decrease in permeability is equal with increasing M1 content for He and N 2 .However, the relative increase in CO 2 permeability with increasing M1 content results in enhanced CO 2 /N 2 and CO 2 /Ar selectivities for all membranes with increasing M1 content, while the corresponding He/CO 2 selectivity decreases for all mem-  Combining the permeation results with WAXS and MAXS measurements shows that for the membranes with 30 wt % M1 both the CO 2 permeability and selectivity (CO 2 / N 2 and CO 2 /Ar) are enhanced, while the layer spacing decreases resulting in lower gas permeabilities with no additional selectivity gain.Because dense membranes separate gases via their intrinsic differences in solubility and diffusivity, the mechanism of permeation and the effect of the layer spacing were studied by measuring gas sorption of CO 2 for all membranes.Subsequently, the diffusion coefficient of CO 2 was calculated using eq 1.Unfortunately, N 2 and Ar sorption were too low to obtain accurate results.Therefore, Table 3 only shows the permeabilities, solubility coefficients, and diffusion coefficients of CO 2 in membranes with M1/M2 compositions of respectively 0/100, 30/70, 50/50, 60/40, and 70/30.Table 3 shows that the obtained coefficients are similar for all compositions, suggesting that the CO 2 permeability mainly depends on differences in solubility.Both CO 2 permeability and solubility increase ∼20% for membranes that contain 30 wt % M1 (3070) compared to membranes without M1 (0/100).This increase in CO 2 solubility most likely arises from the enhanced interaction between CO 2 and the LC polymer and shows the effect of the crown ether moieties in M1.However, the solubility decreases for the membranes that contain more than 30 wt % M1 and further decreases with increasing M1 content.Here, the decreasing layer spacing results in less overall free volume in the polymer matrix that lowers the gas solubility coefficients leading to reduced permeabilities for the membranes containing more than 30 wt % M1.These results show that incorporating crown ether functionalities in LC membranes influences membrane performances by enhancing the chemical interactions between CO 2 and the polymer matrix affecting CO 2 solubility, while the layer spacing of the layered structures influences the membrane performance by affecting the overall free volume and thereby the gas solubility.

Effect of Temperature on Single Gas Performances.
To study the effect of temperature on the single gas performances of LC membranes, He, CO 2 , Ar, and N 2 permeabilities at respectively 20, 40 (below T g ), and 70 °C (above T g ) were measured for membranes with respectively M1/M2 compositions of 0/100, 30/70, 50/50, and 70/30.Because of the long measuring times, the membranes with a M1/M2 composition of 60/40 were not measured.The permeation data are shown in Figure 5 (see Tables S3, S5, and S7 for permeation values).
Figure 5 shows that all gas permeabilities increase with increasing temperature.Especially above the T g of the membranes (70 °C), the gas permeabilities show a large increase.Helium has the highest permeability at all temperatures, followed by CO 2 , Ar, and N 2 .These results can be explained by the effect of a combination of parameters being kinetic diameter, critical temperature, and molecular interactions via the quadrupole moments of the gases (see Table S9 for the kinetic diameter, critical temperature, and quadrupole moments of the gases). 52Helium has the smallest kinetic diameter of all measured gases, leading to a higher diffusion rate through the membranes and therefore the highest permeability of all gases. 52N 2 has the largest kinetic diameter of all measured gases, resulting in the low diffusion rate through the membranes.Combined with a low critical temperature, which leads to a low solubility into the polymer   Contrary to the absolute increase of the permeabilities with temperature, the relative increase of the permeabilities compared to the permeabilities at 20 °C (shown in percentages in Figure 5) shows opposite behavior.Here, N 2 shows the largest permeability increase, followed by Ar, CO 2 , and He.For dense membranes the gas permeability is the product of the solubility and the diffusivity of a certain gas species.Diffusion is generally a stronger function of temperature than the solubility coefficient and typically increases considerably with increasing temperature leading to higher permeabilities with increasing temperature.Less permeable gases, such as N 2 , have higher diffusion activation energies than more permeable gases, such as He, because the diffusion activation energy typically increases with increasing kinetic diameter. 37Therefore, increasing the temperature can elevate the diffusion coefficient of the less permeable N 2 more than the diffusion coefficient of the more permeable He, leading to a relatively higher N 2 permeability increase compared to He.Moreover, the permeation data in Figure 5 show above the T g slight differences in gas permeability for the membranes with different M1/M2 compositions.The membranes that contain more M1 show for all gases a relative higher increase in permeability.For He, Ar, and N 2 this likely arises due the lower cross-link density that decreases with increasing M1 content, resulting in more mobility for the polymer chains and thereby slightly higher permeabilities.However, for CO 2 , increased chemical interactions with the crown ether functionalities above the T g of the membranes can also play a role in the relatively higher increase in CO 2 permeability with increasing M1 content.This is because above the T g of the membranes the increased mobility of the crown ether moieties lead to improved interactions with CO 2 , resulting in a larger increase in CO 2 permeability with increasing M1 content. 53he gas separation performances at the different temperatures were further studied by determining the ideal gas selectivities (He/N 2 , CO 2 /N 2 , CO 2 /Ar, and He/CO 2 ) from the permeation data.These are shown in Figure 6 (see Tables S4, S6, and S8 for ideal selectivity values).
Figure 6 shows that the selectivities toward He and CO 2 decrease with increasing temperature due to a relatively higher permeability increase of the lower permeable gases Ar and N 2 compared to the higher permeable gases He and CO 2 .The He/N 2 selectivity (Figure 6a) shows for all membranes a constant decrease with increasing temperature and is independent of the M1/M2 composition.This is as expected because the crown ether functionalities in M1 have no interactions with He and only slight interaction with the small quadrupole of N 2 , resulting in similar He/N 2 selectivities for all compositions.The CO 2 /Ar selectivity (Figure 6c) also decreases with increasing temperature.Although the M1/M2 composition of the membranes affects the CO 2 /Ar selectivity at all temperatures, the relative decrease with increasing temperature is similar for all compositions.The He/CO 2 and CO 2 /N 2 selectivities (Figure 6b,d) show rather different behavior.Above T g the membranes with higher M1 contents have higher CO 2 permeabilities that result in lower He/CO 2 selectivities but higher CO 2 /N 2 selectivities.To study the effect of temperature in more detail, gas sorption of CO 2 was measured at 6 bar and 20, 40, and 70 °C to determine the CO 2 solubility and diffusion coefficients at these temperatures (shown in Table 4).Because of the long measuring times, the membranes with a M1/M2 composition of 60/40 were not measured.
Sorption measurements in Table 4 show that the solubility coefficient of CO 2 decreases with increasing temperature, confirming that the increase in CO 2 permeability with increasing temperature can be completely attributed to an increasing diffusion coefficient.Membranes that contain 30 wt  , the diffusion coefficients are similar for all compositions, elucidating that for the different compositions the differences in CO 2 permeability mainly depend on the solubility coefficient at a specific temperature.However, above the T g the difference in CO 2 permeability between the compositions is not only dependent on the solubility coefficient but also on the diffusion coefficient.Upon addition of M1, the diffusion coefficient decreases for the membranes with 30 wt % of M1 (30/70) compared to the membranes without M1 (0/100).Surprisingly, the diffusion coefficients of membranes that contain more than 30 wt % M1 increase with increasing M1 content, resulting in the highest diffusion coefficient for the membranes with 70 wt % M1 (70/30).This increase in the diffusion coefficient could be explained as follows.Above the T g largescale segmental motion in the polymer chains results in higher amounts of free volume leading to higher diffusion coefficients compared to below the T g of the polymer.Increasing cross-link density usually result in decreased diffusion coefficients since cross-linking reduces the segmental motion in the polymer chains. 37For the membranes with M1, the cross-link density decreases with increasing M1 content, leading to enhanced diffusion coefficients and thereby higher CO 2 permeabilities and selectivities for the membranes that contain more M1.

CONCLUSIONS
The effect of chemical composition and temperature on gas permeability and solubility in free-standing smectic liquid crystalline (LC) polymeric membranes for gas separations was studied.LC mixtures with various compositions of a monomethacrylate with a crown ether functionality (M1) and a smectic diacrylate (M2) cross-linker were aligned and polymerized, resulting in free-standing membranes with a smectic C morphology and planar alignment.The LC membranes were characterized with POM, DSC and X-ray scattering measurements that confirmed the smectic C morphology for all membranes with different M1/M2 compositions.The tilt angle and the layer spacing of the layered structures are independent of temperature but are highly dependent on the chemical composition.By increasing the M1 content, the tilt angle of the layered structures increases while the layer spacing decreases.Thermal characterization with DSC shows for all membranes a low heat capacity change for the glass transition temperature (T g ) that depending on the chemical composition varied between 46 and 55 °C.
Single gas sorption of CO 2 and permeation of He, CO 2 , Ar, and N 2 at 20 and 40 °C demonstrated that for all M1/M2 compositions the CO 2 permeability mainly depends on a difference in solubility.Both the CO 2 solubility and permeability increased for membranes that contain 30 wt % M1 compared to membranes without M1, leading to improved selectivities toward CO 2 , demonstrating the favorable effect of the crown ether functionalities on the CO 2 gas separation performances.However, for membranes with more than 30 wt % M1, a decreasing layer spacing with increasing M1 content results in reduced gas solubilities that lead to lower gas permeabilities without additional selectivity gain toward CO 2 .Single gas sorption and permeation data from 20, 40, and 70 °C demonstrated that the permeability of all gases increases with increasing temperature, while ideal gas selectivities decrease.Above the T g of the membranes, the CO 2 permeability and selectivity are dependent not only on the solubility coefficient but also on the diffusion coefficient, resulting in higher CO 2 permeabilities and selectivities for the membranes with higher M1 contents.This suggests that above the T g the differences in CO 2 permeability between the different M1/M2 compositions mainly depend on diffusivity rather than solubility.These results show that subtle order differences such as layer spacing in the layered structures also play a role in the gas separation performances of smectic LC polymer membranes.

■ ASSOCIATED CONTENT
* sı Supporting Information The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsapm.2c01154.S1: phase transitions of the used LC mixtures; Table S2: MAXS/ WAXS of LC membranes at 20 and 70 °C; Tables S3− S8: permeability and ideal gas selectivities values measured at 20, 40, and 70 °C; Table S9: kinetic diameter, critical temperature and quadrupole moment of various gas species (PDF)

Figure 1 .
Figure 1.(a) Molecular structures of a monomethacrylate LC with a crown ether functionality (M1, red rods) and a diacrylate LC cross-linker (M2, blue rods).(b) Artist impression of a top and cross-section view of a free-standing membrane with a planar aligned smectic C morphology.(c) Artist impression of a top view of a planar aligned smectic C membrane which indicates the intermolecular spacing, layer spacing, molecular length, and tilt angle of the smectic nanostructure.

Figure 5 .
Figure 5.Effect of temperature on the single gas permeability of (a) He, (b) CO 2 , (c) Ar, and (d) N 2 of LC membranes with various M1/M2 compositions measured at respectively 20, 40, and 70 °C and 6 bar feed pressure.The dotted lines between 40 and 70 °C represent the area where, depending on the M1/M2 composition, the glass transition temperature (T g ) of the membranes is located.The relative increase of permeability compared to the gas permeability at 20 °C is shown in percentage above the columns.The small error bars represent the spread of two independently prepared membranes, where each membrane is measured in triplicate.See Tables S3, S5, and S7 for the values of the error bars.

Figure 6 .
Figure 6.Effect of temperature on the ideal gas selectivities of (a) He/N 2 , (b) CO 2 /N 2 , (c) CO 2 /Ar, and (d) He/CO 2 of LC membranes with various M1/M2 compositions measured at respectively 20, 40, and 70 °C and 6 bar feed pressure.The dotted lines between 40 and 70°C represent the area where, depending on the M1/M2 composition, the glass transition temperature (T g ) of the membranes is located.The relative increase of selectivity compared to the selectivity at 20 °C is shown in percentages above the columns.The small error bars represent the spread of two independently prepared membranes, where each membrane is measured in triplicate.See Tables S4, S6, and S8 for the values of the error bars.

Figures
Figures S1−S5: DSC and POM images of the compounds and mixtures of M1 and M2; Figure S6: FT-IR of an LC mixture (M1/M2 composition of 50/ 50) before and after polymerization; Figure S7: POM images of the prepared membranes; Figures S8−S12: DSC of the prepared membranes; TableS1: phase transitions of the used LC mixtures; TableS2: MAXS/ WAXS of LC membranes at 20 and 70 °C; Tables S3− S8: permeability and ideal gas selectivities values measured at 20, 40, and 70 °C; TableS9: kinetic diameter, critical temperature and quadrupole moment of various gas species (PDF)

Table 1 .
Fabrication Conditions for LC Membranes with Various Compositions of M1 and M2

Table 4 .
CO 2 Permeabilities, Solubility Coefficients Measured at 6 bar and 20, 40, and 70 °C, and the Associated M1 show a decreasing solubility coefficient with increasing M1 content.These results indicate that the decrease of the layer spacing with increasing M1 content leads to lower solubility coefficients at all measured temperatures.Below the T g of the membranes(20 and 40 °C)